English National CurriculumProgramme Of Study For Key Stage 3 Mathematics

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Number (01)

...understand and use place value for decimals, measures and integers of any size

Number (02)

...order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, , ≤, ≥

Number (03)

...use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation property

Number (04)

...use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

Number (05)

...use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals

Number (06)

...recognise and use relationships between operations including inverse operations

Number (08)

...interpret and compare numbers in standard form A x 10n 1≤A<10, where n is a positive or negative integer or zero

Number (09)

...work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7⁄2 or 0.375 and 3⁄8 )

Number (10)

...define percentage as ‘number of parts per hundred’, interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express one quantity as a percentage of another, compare two quantities using percentages, and work with percentages greater than 100%

Number (11)

...interpret fractions and percentages as operators

Number (12)

...use standard units of mass, length, time, money and other measures, including with decimal quantities

Number (13)

...round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures]

Number (14)

Number (15)

...use a calculator and other technologies to calculate results accurately and then interpret them appropriately

Number (16)

...appreciate the infinite nature of the sets of integers, real and rational numbers.

Algebra (01)

...use and interpret algebraic notation, including:
- ab in place of a × b
- 3y in place of y + y + y and 3 × y
- a2 in place of a × a, a3 in place of a × a × a; a2b in place of a × a × b
- a⁄b in place of a ÷ b
- coefficients written as fractions rather than as decimals
- brackets

Algebra (02)

...substitute numerical values into formulae and expressions, including scientific formulae

Algebra (03)

...understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors

Algebra (04)

...simplify and manipulate algebraic expressions to maintain equivalence by:
- collecting like terms
- multiplying a single term over a bracket
- taking out common factors
- expanding products of two or more binomials

Algebra (05)

...understand and use standard mathematical formulae; rearrange formulae to change the subject

Algebra (06)

...model situations or procedures by translating them into algebraic expressions or formulae and by using graphs

Algebra (07)

...use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)

Algebra (08)

...work with coordinates in all four quadrants

Algebra (09)

...recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane

Algebra (10)

Algebra (11)

...reduce a given linear equation in two variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically

Algebra (12)

...use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations

Algebra (13)

...find approximate solutions to contextual problems from given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphs

Algebra (14)

...generate terms of a sequence from either a term-to-term or a position-to-term rule

Algebra (15)

...recognise arithmetic sequences and find the nth term

Algebra (16)

...recognise geometric sequences and appreciate other sequences that arise.

Ratio and Proportion (09)

Ratio and Proportion (10)

...use compound units such as speed, unit pricing and density to solve problems.

Geometry and measures (01)

...derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders)

Geometry and measures (02)

Geometry and measures (03)

...draw and measure line segments and angles in geometric figures, including interpreting scale drawings

Geometry and measures (04)

...derive and use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); recognise and use the perpendicular distance from a point to a line as the shortest distance to the line

Geometry and measures (05)

...describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric

Geometry and measures (06)

...use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles

Geometry and measures (07)

...derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies

Geometry and measures (08)

...identify properties of, and describe the results of, translations, rotations and reflections applied to given figures

Geometry and measures (09)

...identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids

Geometry and measures (10)

...apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles

Geometry and measures (11)

...understand and use the relationship between parallel lines and alternate and corresponding angles

Geometry and measures (12)

...derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons

Geometry and measures (13)

...apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras’ Theorem, and use known results to obtain simple proofs